This course develops the analytical foundations of information theory and statistical inference from the perspective of theoretical physics. Its central theme is the structural equivalence between the mathematical frameworks underlying statistical mechanics and those underlying data inference: the same variational principles that yield equilibrium ensembles also govern optimal inference from incomplete observations.
The course covers Shannon's information measures, the maximum entropy principle and its role in deriving statistical-mechanical ensembles, Bayesian inference and model selection, the Fisher information metric and its geometric interpretation, and inverse problems in which interaction parameters are reconstructed from measured correlations. Throughout, the emphasis is on exact analytical methods rather than numerical implementation or algorithmic recipes
- Dozent/in: Horst-Holger Boltz
- Dozent/in: Thomas Ihle